{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "ResSim_1_Interpolation.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyOGGJDp9peDv4eW5wJs5Eg5",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Divyanshu-ISM/Oil-and-Gas-data-analysis/blob/master/ResSim_1_Interpolation.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LtMr_m869cZe",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gp1yo0KObgQ6",
        "colab_type": "text"
      },
      "source": [
        "#Interpolation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Kc7EsYFCbiXX",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "from scipy import interpolate,integrate"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CQknK6kgbpKJ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x = np.arange(-1,11)"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_RrjZhKqbuD4",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "y = np.exp(-x/3.0)"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jGCqZEAGbyN0",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        },
        "outputId": "11adb293-88c4-47a8-96e5-e23649e15cc9"
      },
      "source": [
        "plt.style.use('fivethirtyeight')\n",
        "plt.plot(x,y)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fdc2560a470>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "M_NcpnMZb8HN",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Step 1: Find the Interpolated Function:"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Dv_9ZbZ1cI_h",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "f = interpolate.interp1d(x,y)"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sPEgGYcWcOZr",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#values from interpolated function\n",
        "l = []\n",
        "for i in x:\n",
        "  v = float(f(i))\n",
        "  l.append(v)\n",
        "\n",
        "y_int = np.array(l)"
      ],
      "execution_count": 27,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "16gsul70cQJO",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 319
        },
        "outputId": "2a7dd3c8-96bf-4e25-e778-a385208c7334"
      },
      "source": [
        "plt.figure(figsize=(10,4))\n",
        "plt.subplot(1,2,1)\n",
        "plt.plot(x,y_int,'r')\n",
        "plt.title('Interpolated function')\n",
        "plt.subplot(1,2,2)\n",
        "plt.plot(x,y,'b')\n",
        "plt.title('Actual Function')\n",
        "plt.tight_layout(False)"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dB6IrGYofwER",
        "colab_type": "text"
      },
      "source": [
        "#Comparing the Actual function and Inerpolated function using integration.\n",
        "We do this since we cannot see any visible difference. Hence The integrated values are the best way to compare"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WFHbDoZ3c-jF",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "bbc7d593-410f-48ae-9e19-5d78e8c1c768"
      },
      "source": [
        "ans,err = integrate.quad(f,0,10)\n",
        "print(f\"1.The integration of interpolated fn gives {ans}\")\n",
        "\n",
        "intg = integrate.simps(y[1:-1],x[1:-1])\n",
        "print(f\"1.The integration of actual fn gives {intg}\")\n"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "1.The integration of interpolated fn gives 2.9197153790964223\n",
            "1.The integration of actual fn gives 2.8550038226912573\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GYNjOLb3dEIT",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Conclusion : Interpolation can be said to be a pretty good estimate of the actual function!"
      ],
      "execution_count": 41,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "R9eS-dy8dFMm",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}